Internal filtration in slurry bubble columns offers a possible solution to the filtration problems related to this reactor type. The applicability of the concept has already been demonstrated at full-scale for wastewater treatment, even though a theoretical description of internal filtration is lacking. Two types of hydrodynamic models were developed for a filtering slurry reactor. Both the model of the surface renewal type and the model based on a force-balance approach predict that the solids concentration at the axial position of the filter uniquely depends on a single novel dimensionless number. The validity of these theories was demonstrated by measuring filter-cake resistance as an indirect measure of solids concentration for a system in batch operation with respect to solids. In the experiments the load of solids, permeate flux (J), superficial gas velocity (Ug), particle diameter (dp), kinematic liquid viscosity (vl), and molar mass of the gas were varied.